Generalized latent variable modeling : multilevel, longitudinal, and structural equation models / Anders Skrondal, Sophia Rabe-Hesketh.

Format:

Book

Author/Creator:

Skrondal, Anders.

Contributor:

Rabe-Hesketh, S.

George R. Fink Memorial Fund.

Series:

Interdisciplinary statistics

Chapman & Hall/CRC interdisciplinary statistics series

Language:

English

Subjects (All):

Latent variables.

Latent structure analysis.

Physical Description:

xi, 508 pages : illustrations ; 24 cm.

Place of Publication:

Boca Raton : Chapman & Hall/CRC, [2004]

Summary:

Exciting and realistic applications demonstrate how researchers can use latent variable modeling to solve concrete problems in areas as diverse as medicine, economics, and psychology.

Contents:

I Methodology xiii

1 The omni-presence of latent variables 1

1.2 'True' variable measured with error 2

1.3 Hypothetical constructs 4

1.4 Unobserved heterogeneity 9

1.5 Missing values and counterfactuals 14

1.6 Latent responses 16

1.7 Generating flexible distributions 17

1.8 Combining information 18

2 Modeling different response processes 21

2.2 Generalized linear models 22

2.3 Extensions of generalized linear models 27

2.4 Latent response formulation 33

2.5 Modeling durations or survival 39

3 Classical latent variable models 49

3.2 Multilevel regression models 49

3.3 Factor models and item response models 63

3.4 Latent class models 74

3.5 Structural equation models with latent variables 75

3.6 Longitudinal models 80

4 General model framework 95

4.2 Response model 96

4.3 Structural model for the latent variables 108

4.4 Distribution of the disturbances 112

4.5 Parameter restrictions and fundamental parameters 117

4.6 Reduced form of the latent variables and linear predictor 120

4.7 Moment structure of the latent variables 121

4.8 Marginal moment structure of observed and latent responses 123

4.9 Reduced form distribution and likelihood 127

4.10 Reduced form parameters 130

5 Identification and equivalence 135

5.2 Identification 136

5.3 Equivalence 152

6 Estimation 159

6.2 Maximum likelihood: Closed form marginal likelihood 160

6.3 Maximum likelihood: Approximate marginal likelihood 161

6.4 Maximizing the likelihood 174

6.5 Nonparametric maximum likelihood estimation 182

6.6 Restricted/Residual maximum likelihood (REML) 184

6.7 Limited information methods 185

6.8 Maximum quasi-likelihood 191

6.9 Generalized Estimating Equations (GEE) 197

6.10 Fixed effects methods 200

6.11 Bayesian methods 204

Appendix Some software and references 216

7 Assigning values to latent variables 221

7.2 Posterior distributions 222

7.3 Empirical Bayes (EB) 225

7.4 Empirical Bayes modal (EBM) 235

7.5 Maximum likelihood 237

7.6 Relating the scoring methods in the 'linear case' 241

7.7 Ad hoc scoring methods 241

7.8 Some uses of latent scoring and classification 243

Appendix Some software 249

8 Model specification and inference 251

8.2 Statistical modeling 251

8.3 Inference (likelihood based) 257

8.4 Model selection: Relative fit criteria 262

8.5 Model adequacy: Global absolute fit criteria 267

8.6 Model diagnostics: Local absolute fit criteria 272

II Applications 283

9 Dichotomous responses 285

9.2 Respiratory infection in children: A random intercept model 285

9.3 Diagnosis of myocardial infarction: A latent class model 288

9.4 Arithmetic reasoning: Item response models 292

9.5 Nicotine gum and smoking cessation: A meta-analysis 299

9.6 Wives' employment transitions: Markov models with unobserved heterogeneity 307

9.7 Counting snowshoe hares: Capture-recapture models with heterogeneity 311

9.8 Attitudes to abortion: A multilevel item response model 315

10 Ordinal responses 321

10.2 Cluster randomized trial of sex education: Latent growth curve model 321

10.3 Political efficacy: Factor dimensionality and item-bias 326

10.4 Life satisfaction: Ordinal scaled probit factor models 338

11 Counts 349

11.2 Prevention of faulty teeth in children: Modeling overdispersion 349

11.3 Treatment of epilepsy: A random coefficient model 355

11.4 Lip cancer in Scotland: Disease mapping 361

12 Durations and survival 373

12.2 Modeling multiple events clustered duration data 373

12.3 Onset of smoking: Discrete time frailty models 375

12.4 Exercise and angina: Proportional hazards random effects and factor models 382

13 Comparative responses 393

13.2 Heterogeneity and 'Independence from Irrelevant Alternatives' 393

13.3 Model structure 395

13.4 British general elections: Multilevel models for discrete choice and rankings 397

13.5 Post-materialism: A latent class model for rankings 404

13.6 Consumer preferences for coffee makers: A conjoint choice model 408

14 Multiple processes and mixed responses 417

14.2 Diet and heart disease: A covariate measurement error model 417

14.3 Herpes and cervical cancer: A latent class covariate measurement error model for a case-control study 422

14.4 Job training and depression: A complier average causal effect model 427

14.5 Physician advice and drinking: An endogenous treatment model 432

14.6 Treatment of liver cirrhosis: A joint survival and marker model 438.

Notes:

Includes bibliographical references (pages 445-485) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the George R. Fink Memorial Fund.

ISBN:

1584880007

9781584880004

OCLC:

54543734

Publisher Number:

99942973676

Online:

Publisher description